Finite Group Databasebeta

← Group #13165689

Character table — Group #13165689

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222444444448888888812121218182424242424242424242424242424242424242424243636363636363636363654547272727272108108
order122236663366666633666666244444666612121212121212121212121212121212448812122424242444266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1111111-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-1-1-111-1-1
χ31111111111111111111111111-1-11111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-1-1-1
χ41111111111111111111111111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-111
χ5111111111111111111111111-111111-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-11111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111
χ7111111111111111111111111-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-1
χ9222222222222222222222222200-2-20222200000000000000000000-2-20000-2-20000000
χ10222222222222222222222222-200-2-20-2-2-2-200000000000000000000-2-20000220000000
χ112222-1-1-1-122222222-1-1-1-1-1-1-1-10222220000-1-1-1-12222-1-1-1-1-1-1-1-10022-1-1-1-1-1-1000000000
χ122222-1-1-1-122222222-1-1-1-1-1-1-1-102222-20000-1-11122-2-2-1-1-1-1111100-2-2-1-11111000000000
χ132222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-2222000011-1-1-2-2221111-1-1-1-100-2-2-1-11111000000000
χ142222-1-1-1-122222222-1-1-1-1-1-1-1-10-2-222-200001111-2-2-2-2111111110022-1-1-1-1-1-1000000000
χ152-22-222-2-222-22-2-2-222222-2-2-2-200000000000000000000000000002−20022−2−22i−2i00000−i2i2
χ162-22-222-2-222-22-2-2-222222-2-2-2-200000000000000000000000000002−20022−2−2−2i2i00000i2−i2
χ172-22-222-2-222-22-2-2-222222-2-2-2-20000000000000000000000000000−2200−2−2222i−2i00000i2−i2
χ182-22-222-2-222-22-2-2-222222-2-2-2-20000000000000000000000000000−2200−2−222−2i2i00000−i2i2
χ192-2-222-22-2222-22-2-2-222-2-222-2-2000-220000000000000000000002i−2i002-20000000002i−2i00
χ202-2-222-22-2222-22-2-2-222-2-222-2-2000-22000000000000000000000−2i2i002-2000000000−2i2i00
χ212-2-222-22-2222-22-2-2-222-2-222-2-202i−2i2-2000002i−2i002i−2i002i2i−2i−2i00000000-220000000000000
χ222-2-222-22-2222-22-2-2-222-2-222-2-20−2i2i2-200000−2i2i00−2i2i00−2i−2i2i2i00000000-220000000000000
χ232-2-22-11-11222-22-2-2-2-1-111-1-11102i−2i2-200000−ii3−32i−2i00−i−iii33−3−300001-1−i3i3−i3i3000000000
χ242-2-22-11-11222-22-2-2-2-1-111-1-11102i−2i2-200000−ii−332i−2i00−i−iii−3−33300001-1i3−i3i3−i3000000000
χ252-2-22-11-11222-22-2-2-2-1-111-1-1110−2i2i2-200000i−i3−3−2i2i00ii−i−i33−3−300001-1i3−i3i3−i3000000000
χ262-2-22-11-11222-22-2-2-2-1-111-1-1110−2i2i2-200000i−i−33−2i2i00ii−i−i−3−33300001-1−i3i3−i3i3000000000
χ27444444441-21-2-21-211-21-21-21-242200011-2-22200-1-100-1-1-1-10000220000000000000-1-100
χ28444444441-21-2-21-211-21-21-21-24-2-200011-2-2-2-200110011110000-2-200000000000001100
χ29444444441-21-2-21-211-21-21-21-2-422000-1-1222200-1-100-1-1-1-10000-2-200000000000001100
χ30444444441-21-2-21-211-21-21-21-2-4-2-2000-1-122-2-200110011110000220000000000000-1-100
χ3144444444-21-211-21-2-21-21-21-21400002-2-211002200-1-10000-1-1-1-10000000000002-1-10000
χ3244444444-21-211-21-2-21-21-21-2140000-2-2-21100-2-2001100001111000000000000-2110000
χ3344444444-21-211-21-2-21-21-21-21-40000222-1-1002200-1-10000-1-1-1-1000000000000-2110000
χ3444444444-21-211-21-2-21-21-21-21-40000-222-1-100-2-20011000011110000000000002-1-10000
χ354444-2-2-2-244444444-2-2-2-2-2-2-2-2000-4-40000000000000000000000000220000000000000
χ3644-4-44-4-4444-4-4-444-444-4-4-4-444000000000000000000000000000000000000000000000
χ3744-4-44-4-44-212-1-1-212-212-12-1-21000000003-3000000−i3i30000−i3i3−i3i30000000000000−i3i30000
χ3844-4-44-4-44-212-1-1-212-212-12-1-21000000003-3000000i3−i30000i3−i3i3−i30000000000000i3−i30000
χ3944-4-44-4-44-212-1-1-212-212-12-1-2100000000-33000000−i3i30000−i3i3−i3i30000000000000i3−i30000
χ4044-4-44-4-44-212-1-1-212-212-12-1-2100000000-33000000i3−i30000i3−i3i3−i30000000000000−i3i30000
χ4144-4-4-222-244-4-4-444-4-2-22222-2-200000000000000000000000000000000i6−i6−i6i6000000000
χ4244-4-4-222-244-4-4-444-4-2-22222-2-200000000000000000000000000000000−i6i6i6−i6000000000
χ434-44-4-2-22244-44-4-4-44-2-2-2-22222000000000000000000000000000022−2200−2−222000000000
χ444-44-4-2-22244-44-4-4-44-2-2-2-222220000000000000000000000000000−22220022−2−2000000000
χ454-4-444-44-41-212-2-12-11-2-121-2-1202i−2i0003-3002i−2i00−ii00−i−iii00002i−2i0000000000000−ii00
χ464-4-444-44-41-212-2-12-11-2-121-2-1202i−2i000-33002i−2i00−ii00−i−iii0000−2i2i0000000000000i−i00
χ474-4-444-44-41-212-2-12-11-2-121-2-120−2i2i0003-300−2i2i00i−i00ii−i−i0000−2i2i0000000000000i−i00
χ484-4-444-44-41-212-2-12-11-2-121-2-120−2i2i000-3300−2i2i00i−i00ii−i−i00002i−2i0000000000000−ii00
χ494-4-44-22-22444-44-4-4-4-2-222-2-222000-440000000000000000000000000-220000000000000
χ508888-4-4-4-42-42-4-42-42-12-12-12-120440000000-2-200-2-200111100000000000000000000000
χ518888-4-4-4-42-42-4-42-42-12-12-12-120-4-4000000022002200-1-1-1-100000000000000000000000
χ528888-4-4-4-4-42-422-42-42-12-12-12-1000004000000-2-200-2-2000011110000000000000000000
χ538888-4-4-4-4-42-422-42-42-12-12-12-100000-40000002200220000-1-1-1-10000000000000000000
χ5488-8-88-8-882-4-2442-4-22-4-24-242-4000000000000000000000000000000000000000000000
χ5588-8-8-444-42-4-2442-4-2-121-21-2-120000000000000000003-33-300000000000000000000000
χ5688-8-8-444-42-4-2442-4-2-121-21-2-12000000000000000000-33-3300000000000000000000000
χ5788-8-8-444-4-424-2-2-4242-1-21-212-10000000000000000−2i32i30000i3−i3i3−i30000000000000000000
χ5888-8-8-444-4-424-2-2-4242-1-21-212-100000000000000002i3−2i30000−i3i3−i3i30000000000000000000
χ598-88-888-8-82-4-2-44-2422-42-4-24-24000000000000000000000000000000000000000000000
χ608-88-888-8-8-4242-24-2-4-42-424-24-2000000000000000000000000000000000000000000000
χ618-88-8-4-4442-4-2-44-242-12-121-21-20000000000000000003i−3i−3i3i00000000000000000000000
χ628-88-8-4-4442-4-2-44-242-12-121-21-2000000000000000000−3i3i3i−3i00000000000000000000000
χ638-88-8-4-444-4242-24-2-42-12-1-21-2100000000000000000000003i−3i−3i3i0000000000000000000
χ648-88-8-4-444-4242-24-2-42-12-1-21-210000000000000000000000−3i3i3i−3i0000000000000000000
χ658-8-888-88-8-42-4-224-24-424-2-424-2000000000000000000000000000000000000000000000
χ668-8-88-44-442-424-4-24-2-121-2-121-204i−4i0000000−2i2i00−2i2i00ii−i−i00000000000000000000000
χ678-8-88-44-442-424-4-24-2-121-2-121-20−4i4i00000002i−2i002i−2i00−i−iii00000000000000000000000
χ688-8-88-44-44-42-4-224-242-1-212-1-2100000000000023−2300000000−3−3330000000000000000000
χ698-8-88-44-44-42-4-224-242-1-212-1-21000000000000−23230000000033−3−30000000000000000000

Here i is the imaginary unit (i² = −1).